Power Strings

Given two strings $a$
and $b$ we define
$a\cdot b$ to be their
concatenation. For example, if $a
= \text {"abc"}$ and $b =
\text {"def"}$ then $a\cdot b = \text {"abcdef"}$. If we
think of concatenation as multiplication, exponentiation by a
non-negative integer is defined in the normal way: $a^0 = \text {""}$ (the empty string)
and $a^{n+1} = a\cdot {a^
n}$.

Input

The input consists of up to $10$ test cases. Each test case is a
line of input containing $s$, a string of lower case letters
(a-z). The length of $s$
will be at least $1$ and
will not exceed $2\, 000\,
000$ characters. A line containing a period follows the
last test case.

Output

For each $s$ you should
print the largest $n$ such
that $s = a^ n$ for some
string $a$.